"Blue Eagle" is an Old-Time breakdown from Texas in D Major. The parts are played AABB. It is a regional Texas tune not well known in other parts of the South.
The tune has been attributed to fiddle player Orville Burns who was born in 1921 in Oklahoma and later moved to Texas. His father suggested the name to him.
The Blue Eagle was the depression era symbol of a thunderbird, employed by companies to show compliance with the National Industrial Recovery Act.
It was printed in Phillips' Traditional American Fiddle Tunes, vol. 1 (1994) and Silberberg's Tunes I Learned at Tractor Tavern (2002).
It was recorded by Lewis Franklin on Texas Fiddle Favorites (1966).
I got this from Adam Hurt and Megan Lynch Chowning's recording on Inside Out (2016). The banjo tab is from Adam Hurt's playing.
The transcription is from John Lamancusa's web site.